Calculator



July l, 1941 A. l.. THURsToN E-rAL 2,247,531

CALCULATOR Filed Aug. 29, 1959 I5, Sheets-Sheet 1 INVENTORS. ARTHUR L HURTON AND BEAUREGARD .SWEENEY July l, 1941- A. THURsToN Erm. 2,247,531

CALCULATOR Filed Aug. 29, 1959 3 sheets-sheet 2 July l, 1941- A. l.. THuRsToN Erm. 2,247,531

CALCULATOR Filed Aug. 29, 1939 3 Shee'LS-Shee'b 3 l .EL

PRESSURE f cARukEl-ER ALTI-rubs 55 INTAKE mn TEMA 600e 90 mulcnnb vAIR SPEED ATTORNEY Patented July 1, 1941 UNITED STATES PATENT OFFICE 2,247,531 CALCULATOR Arthur L. Thurston, Wantagh, and Beauregard Sweeney, Great Neck, N. Y.

Application August 29, 1939, Serial No. 292,380

-23 Claims.

This invention relates to a calculating device for use in controlling the operation of powered craft, with particular applicability to aircraft.

The performance of an airplane is dependent upon a number of variables. In order for the operator to be able to carry out any iiight in the most eflicient manner it is essential that he determine the effect of these variables. He can then adjust those variables over which he has control, -in such a manner as to accomplish the flight in accordance with the requirements and in the most efiicient way consistent with the variables over which he has no control.

The variables which determine the air speed of an airplane in level iiight are: i.

1. The weight of the airplane.

2. The density of the air.

3. The thrust horsepower delivered by the propeller.

'Ihe density of the air is in turn a function of the atmospheric pressure and temperature.

The thrust horsepower is a function oi the engine brake horsepower and the propeller emciency.

The variables which determine the brake horsepower of the engine are the revolutions per min- Aute and the brake mean effective pressure depOWeI.

While the above mentioned variables will determine the airspeed, the operator of the airplane is generally interested primarily in his travel with respect to the earth, not the air.

This is particularly true in scheduled air transport flight, in which a consideration of the motion of the air relative to the ground-the wind velocity and4 directionis essential to' eflicient operation.

In the past, the operator has been obligedv to refer to a series of charts to obtain the information necessary for planning or carrying out a given flight. Calculators have also been devised Y for carrying out certain of the steps in the computations, but the data obtained from them must then be used with the charts in order to arrive at a final solution of the problem.

It is the object of this invention to provide in one instrument a means by which the operator can quickly and readily determine (l) the result of any combination of the variables upon which the performance of the airplane depends,v and (2) the effect of changing each of these variables.

In the calculators previously used, such, for example, as those used for determining the brake horsepower output of the engine, it has been the practice to arrange the instrument in such a way that the resulting data represents the average for theimodel or type, but ma'y be incorrect for the individual airplane or engine which will vary appreciably from the average.

It is a further object of this invention to provide a calculator with a compensating adjustment which can be set and clamped so that the calculator can be adjusted to give correct results for any individual airplane or engine or both.

A further featureof the inventionis that its operation is simple and easy. All the independent variables on the calculator correspond to the readings of various instruments on the airplane. The various curves and indices are arranged to give good intersections and positive readings.

Although the novel features which are believed to be characteristic of this invention will be particularly pointed out in the claims appended hereto, the invention itself, as to its objects and advantages, and the manner in which it may be carried out,.may be better understood by referring to the following description of selected embodiments of the invention taken in connection with the accompanying drawings forming a part thereof, in which:

Fig. 1 is a plan view of one side of a calculator showing the mechanism for determining airspeed and the relation between -'airplane and engine variables and the means for determining flight eiliciency;

Fig. 2 is a side view of the instrument;

Fig. 3 is a plan view of the reverse side of the instrument showing the mechanism for determining the effect of wind on the travel of the aircraft with respect to the ground;

Fig. 4 is a plan view of one side of a calculator similar to that shown in Figs. 1, 2 and 3, but in a slightly modified form adapted for use where fuel economy is of utmost importance, such as long range flights;

Fig. 5 is a plan view of one side of a calculator, also similar to that shown in Figs. 1, 2 and 3, showing a further modification;

Fig. 6 is a modiiied former that section of the instrument dealing only with engine performance;

Fig. 7 is a sectional view of the instrument shown in Figs. 1, 2 and 3, and

Fig. 8 is a view of one side of a calculator similar to that shown in Figs. 1, 2 and 3, but in a modified form adapted for use in cases where the gross weight is subject to wide variation.

Referring particularly to Figs. l, 2, and 3, the calculator combines broadly a support or frame member I, having mounted thereon on one side, and pivotally connected thereto, a rotatable disc 2, an arm 3 and an arm 4, all pivotally connected to the frame member I at the same point I3, and on the reverse side a dial 5 and a transparent arm 5 both pivotally connected to the frame member I at the saule point I6 as the disc 2. On the front side, as shown in Fig. 1, in addition to the pivoted arms 3 and 4, there is also another movable member 1 which is pivotally connected to the frame I at the point 28 independently of the rotatable disc 2 and pivoted arms 3 and `4. Rotatable arm 4 has a slot 0 through which a suitable locking device such as the screw 3, may be inserted, so that the arm 4 may be angularly adjusted with respect to the arm 3, and locked in position with respect to the arm 3, and therealter the arms 3 and 4 will move as a unit. A movable member I is attached to the arm 3, so that it may be moved with respect to the arm 3, either linearly, as shown, or with other motion as required. Mounted on one of these members, such as the pivoted arm 3, may be an efficiency indicator shown at II.

Referring to Fig. 3, which shows the reverse side, there is, in addition to the rotatable dial and the rotatable transparent arm 6, a movable member I2, arranged to move in a guide |3|3. Pivotally connected to the movable member |2 is an arm I4. The pivot, or axis I5, of the arm I4, is so positioned on the movable member I2 and the guide |3-I3 so arranged that as the member I2 is mowed in the guide, this pivot I5 will move along a radial line from the axis IS of the rotatable dial 5.

The upper of the two guide members I3-I3 also serves as a part of the slide rule |1 by means of which any desired supplemental calculations may be carried out, such for example as the total distance traveled and total fuel consumed, as illustrated.

The construction of the modified form of calculator shown in Fig. 4 follows generally that of Figs. l, 2 and 3. The instrument incorporates a frame |0I, rotatable disc |02, rotatable arms |03 and |01, and movable member IIO. In addition, it carries arms ,50 and 5|, pivotally mounted to the frame |0I, by means of the same pivot |I6. Arm 5| is provided' with a slot 58 in which may move the lock screw 59 carried by the arm 50, whereby the arm 5I may be adjusted with respect to the arm 50 and then locked in place so that there-after arms 50 and 5| are rotated as one.

The construction of the calculator shown in Fig, 5 is much the same as that of Figs. 1, 2 and 3. The modification consists of cutting away the left half of the rotatable disc 202 and moving the arm 204 with its locking means 233 and 200 to the right of the pivot 2li.

plishing it should be apparent from the examples set forth above. For example, the arm 12 may be made up of 'two arms adjustable with respect to each other, one part bearing the index arrow 13 and the other the scale 1i.

The calculator shown in Fig. 8 differs somewhat in structure from that of Figs. l, 2 and 3. An additional adjustable member 35 is movably mounted on the base member by means of the screws 33 and 33 insented snugly in holes in the member 35 and moving in the slots 31 and 33 respectively In the base member. Screw 83 also serves as the pivot for the movable member 331. Screw 33 is equipped with a thumb nut for clamping -the member 33 in the desired adjusted position.

'Ihe foregoing describes the mechanical arrangement of several forms of the calculator. As will be seen from the illustrations, the several rotatable discs, arms and movable members" are so shaped and located that scales and curves of the airplane and engine variables and ther/esulting performance may be inscribed 4thereon in desired relation so that the movement of the various members with respect to each other will give the desired information. The character of the scales and curves, the method by which they are. estimated, and the procedure for operating the several examples of the calculator, as given in the descriptive matter which follows, will more fullyexplain the nature of the invention.

Rderring to Fig. l, it will be noted that the rotatable disc has a portion cut away in the upper right sector to provide an edge along which the scale of intake air temperature I3 is inscribed,

f and that in conjunction with this scale there is a family of curves I3 labeled Pressure altitude" inscribed on the frame I. The scale and curves are so arranged that when the disc 2 is rotated 0 until the pressure altitude curve corresponding The calculator shown in Fig. 6 consists of a" support or frame member 10 on which two arms 1I and 12 are pivotally mounted at 13. Although no adjustment is shown, the method for accomto the existing altimeter reading intersects the scale edge at the point corresponding to the existing carburetor air intake thermometer reading, the angular displacement of the disc 2 with respeot to the frame I will represent the eil'ect of the atmospheric pressure (generally expressed as pressure altitude) and the temperature of the air entering the carburetor upon the rake horsepower of the engine.

On the left half of the disc 2 there is inscribed a family of curves 20 labeled "R. P. M." In cooperation with these curves there is provided along the upper edge of the arm 4, a scale of manifold pressure 2|. The right end of the arm 3 is cut away in a series of steps to provide for the inscription of three index arrows, i. e., horsepower 22, percentage of rated power 43, and fuel consumption 46. In conjunction with these indices, there are marked on .the frame I, the corresponding scales 23, 43 and 41.

The curves of R. P. M. and the manifold pressure and horsepower scales, as will be obvious to one familiar with the graphical representation of engine power characteristics, are in eifect merely a transposition to polar coordinates of the usual rectangular coordinate curves of horsepower against manifold pressure at constant R. P. M. Then, if the arm 3 is rotated so that the R. P. M. curve corresponding to the existing -tachometer reading intersects the manifold pressure scale at the point corresponding to the existing manifold pressure gauge reading (the disc z having been adjusted as directed ebevenme brake horsepower may be read on scale 23 opposite the arrow 22.

The R. P. M. curves representing" the average results for a given engine model or series are laid out with the two arms 3 and 4 adjusted to bring t-he screw 9 in the middle of the length of the slot 8. Adjustment of the arm 4 with respect to the arm 3, either side of this mid-position will then compensate for the variation of an individual engine from the average. 'I'hs adjustment may also be used to provide for the gradual loss of power of an engine with length of service.

On the arm 1 there is inscribed a curve 21, which represents the aerodynamic characteristics of the airplane. It will be recognized as a power required curve transposed to polar coordinates. Cooperating with this curve is a scale labeled True Air Speed along the top edge of the slide `IIJ, which is carried on the arm 3, the angular position of which represents the engine brake horsepower.

If the arm 1 were not movable, it would be necessary to provide a family of curves, one

Y for each of several altitudes. If this were done,

it would be observed that all of these curves have almost identical curvature throughout the Y range usually involved in cruising flight and that a single curve placed on a rotatable arm with a proper location for the axis or rotation can be made to coincide with each of these curves. This is done on the calculator by suitably locating the pivot for the arm 1, as at 28.

It will be observed also that the angle through which it is necessaryto rotate the arm to make the single curve coincide with the curve for any l l altitude is a `function of that altitude. On the calculator the upper right portion of the arm 1 is cut away to an edge along which is the air temperature scale 82. Cooperating with this scale, there is inscribed on the frame I, a family of curves 83 labeled Pressure altitude. These curves are so laid out in relation to the air temperature scale that when the arm 1 is rotated to make 'the curve corresponding to the existing altimeter reading intersect the scale 82 at a point corresponding to the existing outside air thermometer reading, the angular setting of the arm 1 will be that required to locate the curve 21 in its proper position for the altitude determined by this pressure and temperature.

To take into account the eiect of gross weight of the airplane upon its airspeed, the slide I0 is provided along its lower edge -with an index arrow 25 which cooperates with the weight scale 26 inscribed on the arm 3. With the arrow 25 set opposite the gross weight on the scale 26 and with the arms 3 and 1 set for engine power and altitude respectively as directed above, the true airspeed of the airplane is given bythe intersection of the curve 21 with the scale 2l..

Since the angular position of the arm 1 is a function of altitude, it may be used to show the relation between true and indicated airspeeds at any altitude. This is done on the calculator byA inscribing on the frame I, the curves of indicated l airspeed 30, in conjunction with the scale of true airspeed 29 marked on the arm 1. These show the relation between True and Indicated Airspeed when the arm 1 is set at the proper Pressure .altitudeV and Outside Air Temperature by means of curves 83 and scale 32.

An eiliciency indicator is shown attached to the arm 3, which has a rotatable disc II pivotally attached to the arm 3. A scale 3| marked "Speed M.P.H..is inscribedon the arm 3; a`scale 32 inscribed marked Gal. hr. inscribed on disc II an index arrow 33 marked Miles per gal. alsoinscribed on disc II; and a miles per gallon scale 34 inscribed on the arm 3. The disc I I is rotated until the number of gallons per hour, on the scale 32, is opposite the number of miles per hour on the scale 3|, and the miles per gallon or efficiency read on the scale 34 at the index 33.

A scale 41 is inscribed on the frame I for use in conjunction with an index arrow 46 marked Fuel consumption on the arm 3. This shows the fuel consumption for a nit of time when the proper setting has been made of the arm 3. In the type of instrument shown in Fig. 1, the fuel consumption is assumed to have a definite relation to horsepower, which is a condition closely approximated by most aircraft. A modiiication of the instrument, to suit conditions where this relationship is not maintained, will be described hereinafter.

'I'he procedure for laying out and locating the various curves and scales is as follows:

- The rst step is the computation of data required for establishing the curves. From test data furnished by the engine manufacturer, determine the manifold pressure required to produce, at sea level and at each of several diierent R. P. M. normally used, each of several horsepowers `within the range of power covered in cruising operation with the given engine. Tabulate the results as in Table I.

Table 1 Manifold pressure at sea level at Horsepower 1600 1700 1800 1900 R. P. M R. P. M. R. P. M. R. M.

fold pressure for a given engine. Tabulate the results as in Table II.

` Table II Brake horsepower at 1800 Std. altitude R. P M. and Increment 28.4 man.

y press.

By means of the formula Actual H. P.

H. P. at standard temperature= /460-I-standard temperature (F.) 460+actua1 temperature (F.)

determine the various combinations of air intakeV each'oi.' several standard altitudes. This determination is made bycomputing the actual temperature required at any pressure altitude to produce a selected horsepower with a combination of manifold pressure and R. P. M. which would produce this power at each of the standard altitudes. The horsepower selected for this computation should be that most commonly used in cruising operation. For example, if 550 H. P. is the selected horsepower and 4000 ft. is one of the standard altitudes considered, then from Table 1I is noted the fact that if the combination of'maniiold pressure and R. P. M. is such as to produce 550 H. P. at 4000 it. standard altitude, it would produce only 530 H. P. at a pressure altitude of 2000 ft. and standard 2000 It. temperature which is 51.9 F. Therefore to produce 550 H. P. with this combination with 2000 it. pressure altitude, the actual temperature must be l -T... -g (400-1-51.0)460 14.9 Similarly with a pressure altitude of 6000 it., the power with standard 6000 It. ,temperature (37.6) would be 570 H. P. and to give 550 H. P. the actual temperature must ne` 2 TWFG?) (460+37-6) -460 73.3

Computations are made for the range of standard altitudes concerned and the results tabulated as in Table III.

Table III Temperature for std. alt. power of 550 H. P. at pressure alt. oi-

Std. alt.

S. L. t000 4000 6000 etc 92.1 123. 6 51.9 82. 6 lll. 9 i4. 9 44. 7 73. 3 19. 2 9. 8 37.6 -50. 22. 3 4.8

From airplane data which is usually furnished by the airplane manufacturer in the form o! a curve of brake horsepower required vs. speed-in level ilight at some standard altitude-generally sea level-with normal gross weight. compute horsepower vs. speed at other standard altitudes using the formulae wherein V1 and HP1 are respectively the speed and the horsepower at an altitude of density p1 and V: and HP: are the corresponding values at a density pa. Tabulate the results asin Table IV.

Determine the various combinations of pressure-expressed as pressure altitudeand air temperature which are equivalent to each standard altitude. For this use standard altitude data universally available and the formula wherein =re1ative density (which deilnes the std.

alt.)

P=atmospheric pressure in ins. Hg T=air temperature in degrees F.

Tabuiate the results as in Table V.

Table V Temperature for std. alt. with pressure alt. oi

Btandardaltltude s L. zooo 4000 e000 sooo 50.0 1211 13.0 etc. 99.1 51.9 15.4 19.1 au 44.1 a4 21.0 15.5 31.6 1.3 106.0 08.5 30.5

Compute horsepower vs.` speed in level flight at the average standard altitude for cruising operation with each of several gross weights, using the formulae n.. 15) an: my" V. W. and HP. W.

wherein V1 and HP1 are the speed andhorsepower with gross weight W1 and Vn and HP2 are corresponding values for gross weight Wa. Tabp-l and HPH- l 00 V1 p2 HP. p2 ulate results as in Table VI.

` Table vr Brake horsepower and speed 0 6000 it. with poes weight 0l- Wa 'l' W4 l Wa Wl H (mm Tabl@ 1v) Wx) =.101 W1 .013 Wl .544 W1 :.811

13. H. P. M. r. n. n. H. P. M. r. n. BJB. P. M. P. n;

311 ns1 124 v205 111 431 141. s ses 1x4. s 214.5 120.1: 484.5 15s :caseta 144.5 204 120 TAS TASO X wherein TAS=true airspeed atl altitude, corresponding to a given indicated airspeed TASo=true airspeed at sea level corresponding to said' indicated airspeed 4 -relative air density at said altitude Tabulate the results of computations as in Table VII.

forward and obvious.

position of the working index make a working mark on the base correspondingly labelled 2, 4, etc.

Set the working index at one of the standard altitude working marks and, using the data from Table III, mark a point on the base along the edge of the scale I9 at the temperature required to give the selected power at each of the several pressure altitudes. Repeat the operation for each of the standard altitudes and join the points pertaining to each pressure altitude, obtaining the family of curves I8.

'Ihe scales 3|, 32 and 34 are logarithmic, the combination being that of a circular slide rule for computing the-miles per gallon from the formula miles per hour The layout of the scales 49 and 41 in conjunction with the indices 48 and 46 is straight- Table VII Stamm True air speed for an indicated air speed oilwi i u e M. P H. M. P. H. M. P. H; M. P. H. M. P. H. M. P. H.

S. L.. 1. 00 142. 3 151. 9 161. 5 171 180. 6 190 2000. 1. 030 146. 6 156. 7 166. 5 176. 3 186 195. 7 4000. 1 061 151. 2 161. 3 171. 5 181. 6 191. 8 201. 3 6000` 1. 094 155. 8 166. 2 176. 9 187. 0 197. 3 207. 6 etc.

The data having been obtained, the next step is the laying out of the various curves and scales. There is nothing arbitrary about the size and shape of the various members but -the general configurations shown will be found to give good intersections and easy reading.

The horsepower scale 23 is laid out on the base I, as shown, with uniform spacing and using about '75 of arc to `cover the range of power which may b e used in cruising operation. Scribe also the horsepower index arrow 22 on the edge 4: of arm 3, as shown. Scribe the uniformly spaced scale of manifold pressure 2l to include the extreme values determined in the. computations. Tighten the screw 9 in mid-position in the slot 8.

Mark the uniform temperature scale i9 along 5H the edge of the disc as shown, rotate the disc so that this edge slopes upward to the left by about 10, and clamp the disc to the base. Move arm 3 to bring the index 22 to a reading on scale 23 corresponding to one of the horsepower values t5 used in the computations. Using the data from Table I, mark a point on the disc 2 along the edge of scale 2| at the manifold pressure required to producethis horsepower atv each of the several R. P. M. considered. Repeat this operation for each of`the other horsepowers considered and draw a curve through the points pertaining to each R. P. M. The result will be the family of curves 20.

Set theY indexV 22 at the sea level power used G5 in the computations of Table II and clamp the arm 3 to the disc 2. Mark a temporary or working index on disc ,2 at any convenient pointgenerally on the left side-and opposite this index on base Il indicate a temporary or working mark labelled S. L. Release the clamp holding the disc to the base and move the disc-and arm 3 secured to it-to set the index 22 successive] at the values obtained in Table II at standard altitudes of 2000ft., 4000 ft., etc. and at each F'orv the airplane performance portion of the calculator, scribe the uniform airspeed scale 24 on the edge of the slide I0, as shown. If the performance computations have been carried out with normal gross weight, set the slide toward its extreme left position; if an average gross weight was used, set the slide in mid-position.

Fasten the member 1 in some arbitrary position on the base, marking a working index along the edge of the member vat a. convenient point and corresponding working mark, labelled 5000, opposite it on the base. Using the data from Table IV, set the index 22 at the horsepower corresponding to a given speed-with the gross weight'used for the computationsat 5000 ft. (the average altitude anticipated in cruising op' eration) and mark a point on member 1 along the edge of the scale 24 at that speed. Repeat the operation for other-speeds at said altitude and join the points to obtain curve 21.

The location of the pivot point is determined by trial. Try some point in the general location of that shown at 28. Set the index 22 at the power corresponding to some speed at sea level and rotate member 1 about the trial pivot until the curve 21 intersects the scale 24 at that speed. Hold member 1in this position andl check the pivot location by moving arm 3 to bring the index 22 to the power corresponding to the several other speeds at sea level and noting whether the curve 21 intersects the scale 24 properly at these speeds. Repeat for other standard altitudes. After a few tries a pivot point location will be found such that by rotating member 1 about it the curve 21 will be sofpositioned as to give readings of airspeed checking with the computed values atall altitudes within plus or minus one M. P. 'Hf

Having properly located the pivot point rotate member 1 to positions corresponding to the several standard altitudes and opposite the working true course index I3. Arm 6 is rotated until its arrow 31 is over the degree mark on the dial l from which direction the wind is blowing.

of member 1, as shown. With member 1 Vset to bring the working index to each oi the standard altitude working marks, mark points on the base along the edge of scale I2 at the temperatureobtained from Table v -which, with each of the pressure altitudes used, will give the standard (density) altitude at which member 1 is set. Join the points pertaining to each pressure altitude, to obtain the family oi curves 83.

Scribe the airspeed scale 28 along the edgeoi member 1 as shown. With the working index again set at each of the standard altitude work ing marks and using the data from Table VII, mark a point on the base along the edge oi' scale 2l at the true airspeed corresponding to each of the several indicated airspeeds at the altitude at which member 1 is set. Join the points pertaining to each indicated airspeed to obtain the family o! curves 30.

Set the member 1 at the average altitude selected for the computations and set the indexr22 atthe selected power. Scribe the gross weight index 2s on the slide lo as Shown and opposite it on the arm 3 scribe a line which is labelled with the gross weight used in the computations. With the other members stationary, move the slide I until the curve 21 intersects the scale 24 at a speed corresponding to each of the other gross weights for which computations were made as per Table VI. Scribe a line on the-arm 3 at each of the corresponding positions of the index 25 and label these lines with the appro' priate gross weights.

The several working marks and indices may then be removed.

Referring to Fig. 3, which shows the mechanism for determining the effect of the wind on the performance of the aircraft with respect to the ground, the rotatable dial 5 has inscribed around its edge a scale 35, of degreesirom 0 to 360, lcommonly .called a compass rose.` The transparent rotatable arm l has a velocity scale 3l inscribed on it along a line extending radially from its pivot Il and vending in the arrow point 31. The sliding member I2 has inscribed thereon an index arrow 3B, marked "ground speedf which is used in conjunction with the scale 2l on the upper guide I3. The arm I I, which is piv otally connected to the sliding member I2 at Il, has a scale Il marked True air speed" inscribed along its upper edge which is on a radial line from the pivot I 5. The arm il also has a protractor 4I marked Angle of drift "Right and "Left An index arrow l2 is inscribed on the member I2 which is used in conjunction with the "Angle of drift protractor 4I. An index arrow 43, marked "True course" is inscribed on the frame I at the edge of the dial i and in a straight line with pivot points II and I i. 'I'he velocity scale Il, the true airspeed scale Il, and the ground speed scale 3l, are all Amade to the same scale or reduction. The ground speed index 38 and scale .Il are so arranged that they register the distance,to the speed scale, between the pivot points Il and Il. The true airspeed scale ll is laid out with its "0 at pivot point Il, that is, it registers the distacealong a radial line from pivotl point Il. Thelvelocity scale il also registers the distance along a radial line from the pivot point Il.

The slide I2 and arm Il are moved until the true airspeed of the plane on the scale 40 intersects the scale 36 at the existing wind velocity, as at the point 4|. The ground speed is read on the scale 39 at index arrow 38. To determine the proper heading for the aircraft to make the course good, the angie of drift is read on the drift protractor 4I at index 42 and added to the true course angle if it is left drift and subtracted` from true course angle if right drift.

In this operation it can be seen that a vector diagram, consisting of the triangle whose vertices are the points I5, I6 and 44, is set up and solved. The ground speed vector is represented by the distance between I5 and I6; the wind velocity vector is represented by the distance between It and Il; and the true airspeed vector is represented by the distance between -IS and M. The angle of drift shown on the protractor 4I at index 42 is the same as the angle between a linefrom I! to I6 and a line from I5 to Il. When the settings are made on the .dial 5 and the arm I, the angle between a line from I6 to 43 and a line from I6 through M to 31, is the angle between the wind and the desired course.

Above and below the true course index Il, Fig. 3, are scales 45 inscribed on the frame I marked "double driit, "right" and 1eft. These are used in connection with the so-called "double drift method of determining an unknown wind direction and velocity. The procedure lnvolves a knowledge of the true airspeed and measurement-by means such as a drift indicator-oi.' angle oi drift when ilying on each of two headings at an angle to each other.- The dial l is rotated so that the ilrst heading of the aircraft on the scaleL 35 is opposite lthe mark on the scale ll corresponding to th angle of dritt obtained on the iirst heading. The member I2 is moved so that the index arrow 3l is opposite the true airspeed on the scale ll. The arm Il is rotated until the index arrow l2 is opposite the angle of drift obtained on the ilrst heading on protractor II. A pencil line is marked on the dial 5 along the upper edge of the arm Il. Sucha line is shown as ll. Ihe dial l is next rotated until the second heading on the scale Il is opposite the angle of drift. obtained on the second heading, on scale Il. The member I2 is moved so that the index arrow 2l is opposite the true airspeed on the scale' It. While usually the -true airspeeds are the same on both headings they need not necessarily be so. The arm Il is rotated until the index arrow l2 is opposite the angle of dritt, obtained on the second headingnon the protractor 4I. A second pencil line is drawn on the dial l along the upper edge o! the arm I4. Such a line might be along they edge of the'arm Il as shown in Fig. 3. The intersection of the two lines would then be at the point M. The arm l is then rotated until the line from II to l1 is over the intersection oi the pencil lines at Il) The windyelocity isthen read on the scale oi' the transparent arm t at the intersection M of the pencil lines. The direction from which the windisblowingisreadonthescalel! onthe dialv l at the point of the arrow I1 on the transparent arm i.

'Ihsmodincationshowninl'ig.4isonethat applies particularly to the long range type oiA aircraft where fuel economy is of great importance. The calculator, of which one side is shown, was designed for use in connection with an engine which is operated in cruising flight at one of three manifold pressures, the desired power at the selected-manifold pressure being obtained by suitably varying the R. P. M. The operation of the arm |01 in cooperation with the arm |03 is the same as previously described for Fig. 1. The method of determining engine power and the effect of engine variables is somewhat different, however, as will appear from the following description. On the arm 50, there is inscribed an index arrow 52 marked Intake air temperature used in conjunction with the scale 53 inscribed on the frame |01. The arm 5| has inscribed on it an index arrow 54 marked "Manifold pressure" oppose which any one of the index arrows, 55, 56 and 51, marked 26 MP," 25 MP- and 24 MP respectively, inscribed on the disc |02, may be placed by rotating this disc. The arm 5| is provided with a slot 56 and a locking screw 59 by means of which thearm 6| may be adjusted with respect to the arm 50, to take care of the variations of a particular engine or group of engines from the average, and then locked in place so that thereafter the arms 50 and 5| are rotated as one.

The arm |03 has inscribed on it a pressure altitude scale 60, to the left of the axis ||6, and another pressure altitude scale 6| to the right of the axis IIE. With arms and 5| set in the proper position as determined by index 52 and scale 53, and with the disc |02 set so that index 55 on the disc is opposite index 5| on the arm 5|, curves of R. P. M. 62 on disc |02 are used in conjunction with the pressure altitude scale 60; the angular displacement of the arm |03 being a function of the horsepower such as is shown by the horsepower index |22 and scale |23. At the same time the fuel consumption curves 63 are used in conjunction with the other pressure altitude scale 6I. When the disc |02 is rotated to bring the index I6 on the the R. P. M. curves 65 and a third set -of fuel consumption curves (also not visible) are used.

While the procedure for laying out that por- `tion of the calculator which deals with airplane performance is the same as that used for the I calculator of Fig. 1, the engine portion is laid out in a somewhat different manner. Y'I'he data usually furnished by the engine manufacturer generally consists of a set of curves ior each of the three manifold pressures to be rused, which in the examples shown are 24,25 and 26 inches Hg. These curves-or tables-give the power output of the engine with aconstant intake air temperature and with varying R. P. M. and pressure altitude. From these data determine the pressure altitude at which each of a number of horsepowers in the cruising range will l*be produced with each of several R. P. M. used for cruising. This determination is made for each of the manifold pressures used.

The engine manufacturer also furnishes fuel consumption data in the form of specific fuel consumption curves superposed upon the aforementioned power-pressure altitude-R. P. M.

curves. First compute the power required with each of several specific fuel consumptions to give each of several values of consumption in gallons per hour. The formula used is the same as that given above for the fuel consumptions for the calculator of Fig. 1. The resultsin the case of a two-engined planeare tabulated as in Table VIII.

Table VIII yCorresponding B. H. P. per engine, with spec. fuel cons. of-

Gals. per hour '.43 .44 .45' .46 41,etc.

558 545 533 l522. 510 7B 544 632 620 509 76 530 518 507 495 485 etc. Then on the graphs for each manifold pressure, plot a point on the .43 specific consumption curve at 558 H. P., on the .44 curve at 545 H. P., on the .45 curve at 533 H. P. etc. to give a curve showing the relation between H. P. and pressure altitude fora consumption of 80 gal. per hr..

The corresponding curve for 78 gal. per hr. is obtained by plotting a point on the .43 specific consumption* curve at 544 H. P., one on the .44 curve at 532 H. P. etc., and joining thesepoints. Similar curves are plotted for the several other values of fuel consumption.

Correction for' variation from constant air intake temperature is made on the basis of the approximation that 10 F. Variation in temperature will change the horsepower by 1%,v an

increase in temperature resulting in a. decrease in power and vice versa.

To layout the curves and' scales, set screw 59 in mid-position in slot 58 and thereafter move arms 50 and 5| together. .Mark the manifold pressure index 54 on arm 5| as shown and the air intake temperature index 52 on arm '50 as shown. Set the arms 50 and 5| approximately as shown and opposite the index 52 mark a line on base |0| labelled with the constant air intake temperature normally used in operation. Clamp the arms to the base in this position. Scribe the three manifoldpressure indices 55, 56 and 51 on the disc |02 at approximately 60 intervals and label them with the appropriate pressure yvalues to be used.' Scribe the horsepower index |22 on the arm |03 and the uniform power scale |23 on the base as shown. Scribe the uniform pressure altitude 60 and the telescoped scale GI-arr approximation to logarithmic spacing will give a convenient arrangement of the curves 63-on the edges of the arm |03 as shown.

Set one of the manifold pressure indices on disc |02 opposite the index 54 and set the horsepower` indexY |22 at one of the powers used in the computations for the manifold.' pressure. Along the edge of the scale 60 mark a vpoint on disc |02 at the pressure altitude at which this power will be produced at each of theseveral R. P. M. Also along the edge of the scale 6| mark a point on the disc at the pressure altitude at which this power will require each of the several fuel consumptions. Repeat for other powers and join the points pertinentY to each R. P. M. and fuel consumption to 'give the families of curves such as 62 and 63. Repeat for the ther manifold pressures.

Set index |22 at the power most commonly used in cruising operation, clamp arm |03, disc |02 and arms 50 and 5| together, and release the clamp holding arms 50 and 5| to base ,|0l. Move index |22 to a power 1% greater than that selected and-opposite the index 52 mark a line on base labelled with a temperature 10 F. less than the constant value. Repeat with powers 2%, 3%, etc. greater making marks on the base labelled 20, 30, etc. less than the constant temperature and with powers 1%, 2%, etc. less than that of the selected power, making marks labelled 10, 20, etc. greater than the constant temperature.

Fig. 5 shows one side of a calculator similar to that shown in Figs. l, 2 and 3, but with the engine power unit modified to provide a determination of brake means effective pressure. The

establishment of pressure altitude curves 2|34 in conjunction with the air intake temperature scale 2|3 and of the R. P. M. curves 220 in conjunction with the manifold pressure scale 22| is the same as described above for the construction shown in Fig. 1.

In the space made available by the cutting away of the left portion ofthe disc 202, curves of B. M. E. P. 31, and fuel consumption 63 are inscribed on the frame 20|, in conjunction with the scale of R. P. M. 06 along the top edge of the arm 203. These curves are merely transposition to polar coordinates of curves of R. P. M.

against brake horsepower at constant fuel flow and constant B. M. E. P. 'A limit curve such as 30 may be superimposed on` the B. M. E. P.

curves for the purpose of showing the maximum y B. M. E. P. permissible at any R. P. M.

The procedure for laying out this calculator is the same as for that of Fig. 1, except for the curves of B. M. E. P. 61 and fuel consumption 33. Data for the former are obtained by using the formula y I Merli B, M E. P.R p M Xdisplacement 6 deals only with engine power and the variables affecting it. The instrument shown is for use with an engine having two different supercharger drive gear ratios. From-the following description of the nature of the various curves and scales and in the light of the directions set forth above for the other calculators, the procedure for laying out this calculator will be obvious.

The curves of pressure altitude 13 on the frame 10 in conjunction with the scale 14 on the arm 1| are establishedin the same manner and serve the same purpose as the corresponding curves |3 and scales |3 of Fig. 1.

The same is true of the R. P. M. curves 11 and 13 inscribed on the frame 10, in conjunction with the manifold pressure scale 13 marked on the arm 12, except that there are two families of curves, one 11 labeled "Low blower for use when the low ratio supercharger drive is engaged and the other 13, labeled High blower" for use when thek high gear ratio is engaged. The index 13 labeled Horsepower" onthe arm 12 reads on the horsepower 'scale 33 and fuel consumption scale 3| marked on the arm 1|.

of gross weight. In the embodiment shown, the

means for the determination of engine power output are similar to those described above, except that the plotting is reversed. Curves of intake air temperature 39 are plotted on the base 30| and the scale 03, along the edge of the cutaway portion of the disc 302, is that of pressure altitude. Similarly the curves of manifold pressure 3l and 01 are plotted on the disc 302, for cooperation with the scales of R. P. M. 04 and 33 inscribed along the edge of the arm 303. The index arrow 322 and horsepower scale 323, however, are similar to those previously described.

Curves 'of pressure altitude $3, inscribed on the base member 30|, are laid out in cooperation with the scale of R. P. M. 92 marked on the edge of thearm 303, in such away as to make possible the determination of the altitude at which full throttle opening is required in order to develop, at any R. P. M., the power indicated by any angular position of the arm 303, and hence the altitude above which the pilot should shift to the high blower gear ratio in order to be able to maintain that power at that R. P. M.

As has been noted above, for moderate variations in gross weight, the radial shifting of the airspeed scale 24-by sliding the member |3- with respect to the power required curve 21 is sufficiently precise for all practical purposes. In cases where the gross weight varies widely, however, a more exact shifting of the one with respect to the other is desirable; This is accomplished in the device or Pig. 8 by shifting the 'is inscribed on the arm 301, as in the calculator of Fig. 1. The corresponding curves of indicated airspeed 330 and pressure altitude 333, however, are inscribed on the added adjustable member 3l. On this member there is also marked a gross weight index 33 which reads on the gross weight scale 3| marked on the base member 30|. As may readily be seen, the movement of the member 35 is governed by the travel of the screws 33 and 33 in the slots 31 and 30, and when member 35 is moved it carries with it the scales 323 and 332 and the pivot 33 for the arm 301. Thus the curve 21 is shifted with respect to the scale 323. The markings 33 and 3|, the slots 31 and 33 and the screws 33 and 33 are so arranged that this shift accurately represents thew efl'ect o'f gross weight on power required.

If the index 30 is set opposite the pertinent gross weight on scale 3|, computations involving airspeed, power, altitude, etc. may be made by manipulation of members 332, 303 and 331 as set forth above and the results will be accurate for flight at that weight.

The data to be computed for this calculator are the same as for that of Fig. 1 except that instead of determining the manifold pressure required to 'giye a certain power at a certain R. P. M., it is expedient to determine the R. P. M'. required to give that power with a certain manifold pressure. Similarly instead of computingl air intake temperatures for a certain pressure altitude, the temperature is assumed and the'al- Y calculator pertaining to engine power is similar to that used in the Fig. 1 construction. The airplane perfomance portion is laid out somewhat differently as follows:

Fasten a piece of drawing papervon the base 30|. Then using the airspeed scale 324 and the H. P. scale 323 with the index 322,`and using data such as in Table IV, plot on this paper a family of power curves like the curve 321, one each for S. L., 5000 ft., 10,000 ft., etc. and with the normal-or average-gross weight. On a piece of tracing paper, 'trace the curve for an average altitude of cruising operation, say 5000 ft. Then by trial and error locate a pivot point 86 such that when the tracing is rotated about this point the traced curve will superpose on each of the curves plotted on the paper. Mark an altitude reference index on the tracing and under each of the positions of this index corresponding to superposition of the traced curve on an altitude power curve, make a reference mark on the paper labelled with the appropriate altitude. c

' Plot on the paper, as above, but using the data such as that in Table VI, a family of curves of power at the average altitude with the various gross weights. Mark a reference point such as 88 yand an index such as 90 on the tracing and shift the tracing so as to make the traced curve superpose on the several curves of this family.

For each such superposed position make a mark on the paper under the points 86 and 88 on the tracing and opposite the index 90l mark'a line labelled with the appropriate gross weight. J

Transfer from the tracing to member 301 the traced curve as 321, the pivot point 86 and the altitude reference index. Transfer from the tracing to m'ember85 the points'86 and 88 and the gross weight index 80. fer to the member 85 the altitude vreference marks and transfer to the base 30| the various positions of the points 86 and 88 and the gross weight marks as at 9|. A line joining the various positions of the point 88 on the base determines the center line of slot 89, while the line through the various positions of point 86 determines the centerline of slot 81.

From the paper transe The scales 382 and 329 are scribed, and the curves 383 and `330 laid out with the vaid of the standard altitude reference index and reference r marks in the manner prescr bed for the corresponding curves 83 and 30 ofFig. 1.

In any of the embodiments shown in Figs. 1, 4, 5 and 8, additional calculations may be made possible by making the disc 2 transparent and inscribing under it on the base member I, additional curvessuch as fuel consumption curves, for examplewhich can be used in cooperation with the scales inscribed along the upper edge of the arm 3.

A better understanding of the nature of the invention may be obtained from an illustrative example, as shown in Figs 1 and 3. It should be understood that the sequence of operations may be changed to fit any particular set of conditions. It is alsoassumed that the. arm 4 has been suitably adjusted With'respect to nthe arm 3 and vlocked in positio It is desired to fly on a course of 340 over the ground and maintain a speed overthe ground of 150 M. P. H. The altimeter registers 4000 feet (pressure altitude) and the outside air temperature is 'I'he carburetor intake air is being heated to The wind velocity at this altitude 9 is 3o M. P. H. from 265. The gross weight or the aircraft is 8000 lbs.

`We wish to determine:

1. What speed relative tothe air (true -air speed) is necessary to maintain the M. I. H.

ground speed.' f

2. What direction should the aircraft be headed.

3. What the manifold pressure should be for 1900 R. P. M.

4. What is the fuel consumption. 5. How many miles over the ground will be made for each gallon of fuel. f 6. What should be the airspeed meter reading (indicated airspeed).

'7. What horsepower is required.

8. What percent is this of the rated horsepower of the engine or engines.

OPERATION Move member I2 until ground speed index 38 is opposite 150 on scale 39. Rotate arm 6 until index arrow 31 is over 265 on scale 35 on dial 5. Rotate arm I4 until its upper edge intersects scale 36 on arm 6 at the 30 mark- At this intersection readon scale 40 that the speed through the air (true air speed) must be M. P. H. (Item 1.)

Read on the protractor 4| opposite index 42 that the angle of drift is 10? right Subtract this 10 from the true course of 340 giving 330 which the aircraft must be headed (Item 2).

Turn to the other side of the instrument as shown in Fig. 1. dex arrow 25 is opposite the 8000 mark on scale 26. Rotate disc 2 until the line .marked 4000 of the pressure altitude lines I8 intersects the intake air temperature scale I9 at the 60 mark. Rotate arm 1 until the line marked 4000 of the pressure altitude lines 83 intersects the outside air temperature scale 82 at the 40 mark. Rotate the arm 3'until the curve 21 intersects the true airspeed scale 24 at the 160-mark. Read at the intersection ofthe 1900 line of the R. P. M. lines 20 and the manifold pressure scale 2|, that 26 inches of manifold pressure are' required (Item 3). i.

Read on scale A41 opposite the fuel consumption arrow 46, that 40 gallons per hour will be used l (Item 4).

Rotate disc I I until the 40 mark on scale 32 is opposite the 150 mark on scale 3|. Read on scale 34 opposite the indexl arrow 33 that 3.75 miles over the ground4 will be made for each gallon 'of fuel (Item 5).-

Opposite the 160 mark-on scale 29 read that Knowing vthe ground speed and fuel consump-v Vtion` the time to go any distance and the total fuel required may be calculated on the slide rule I1.

. While we have described ourfinvention in detail 1n its present preferred embodiment, it will be obvious to those skilled in the art, after under- Move member I0 until the ini standing our invention, that various changes and modifications may be made therein without departing from the spirit or scope thereof. We aim in the appended claims to cover all such modifications and changes.

We claim as our invention:

1. In a calculator, a first member having'inscribed thereon a family of curves and a scale, a

- position the markings thereon indicate the relationship between several factors of a given problem.

2. In a calculator, a first member-having inscribed thereon two different families of curves, a second member mounted on and movable relatively to said first member, said second member having inscribedthereon a curve and also markings adapted for-#cooperation respectively with the families of curves inscribed on said first member, and a third member movable in relation to said second member, said third member having inscribed thereon markings adapted for cooperation withthe curve inscribed on said second member lwhereby when all of the aforesaid members occupy a particular position the markings thereon indicate `the relationship between several factors of a given problem.

3. In a calculator, a first member having inscribed thereon two different families of curves, a second member mounted on and movable relatively to said first member, said second member having inscribed thereon markings adapted for cooperation with one of said families of curves, a third member mounted on and movable relatively to said first member, said third member having inscribed thereon markings adapted for cooperation with the other of said families of curves, said second and third members each having inscribed thereon one or more curves, and a fourth member mounted on and movable relatively to said first member as well as relatively to the secondl and third members, said fourth member having markings inscribed thereon for cooperation respectively with the curves inscribed on said second and third members whereby when all of the aforesaid members occupy a particular position the markings thereon indicate the relationship between several factors of a given problem.

4. In a calculator, a first member having inscribed thereon separate groups of face markings, a second member and a third member fastened to and independently movable in relation to said rst member, each said ,second and third members having inscribed thereon edge markings and also face markings, the edge markings being adapted for cooperation respectively with the separate group markings inscribed on said rst member; and a fourth member fastened to said first member and movable relatively to said second and third members as well as relatively to said first member, said fourth member having inscribed thereon markings adapted for cooperation with the face markings on said second and third members as Well as with certain of the face markings on said lfirst. member whereby when all of the aforesaid members occupy a particular position the markings thereon indicate the relationship between several factors of a given problem.

5. In a calculator, a first member having inscribed thereon at least three separate groups of face markings, separate side by side members fastened to and independently movable relatively to said first member, each of the side by side members having inscribed thereon edge markings and face markings, the edge markings being adapted for cooperation respectively with two of the separate groups of face markings inscribed on the first member, and a fourth member fastened to said first member and adapted to extend spanwise across the side by side members, the fourth member being freely movableand having inscribed thereon at least three markings adapted for cooperation respectively with the face markings on said side by side members and with the third face marking on said first member whereby when all of the aforesaid members occupy a particular position the markings thereon indicate the relationship between several factors of a given problem.

6. In a calculator, a first member having inscribed thereon a plurality of scales, a second member carried by and rotatable in its relation to said first member, said second member having inscribed thereon a family of curves, and a third member carried by and rotatable in its relation to said first and second members, said third member having inscribed thereon markings adapted for cooperation with said family of curves and also indices adapted for cooperation respectively with said plurality of scales whereby when all of the aforesaid members occupy a particular-position the markings thereon indicate the relationship between several factors o a given problem.

7. In a calculator, a rst member having inscribed thereon two different families of curves and a scale, a second member. movable relatively to said first member, said second member having inscribed thereon markings adapted for cooperation respectively with said two families of curves and also having inscribed thereon at least one curve, and a third member movable in relation to said first and second mem-bers, said third member having inscribed thereon segregate markings adapted for cooperation respectively with thev scale on said rst member and with the curve inscribed on said second member whereby when all of the aforesaid members occupy a particular position the markings thereon indicate the relationship between several factors of a given problem.

8. In a calculator, a first member having inscribed thereon two groups of face markings, a second member movable in relation to said first member, said second member having inscribed thereon an edge marking adapted for cooperation with one of -the two groups of face markings inscribed on said first member and also having inscribed thereon a face marking, a third member movable in relation to said first member, said third member having inscribed thereon an edge marking adapted for cooperation with the other group of face markings inscribed on said first member and also having inscribed thereon a face marking, and a fourth member movable in rela.- tion to the other three members, said fourth member having inscribed thereon segregate edge markingsl adapted for lcooperation respectively markings adapted for cooperation with the other adapted for cooperation respectively with the one with the face markings on said second and third members whereby when all of the aforesaid members occupy a particular position the markings. thereon indicate the relationship betweenseveral factors of a given problem.

9. In a calculator, a first member, a second member having inscribed thereon a face marking, a third member having inscribed thereon a face marking, each said second and third member being movable in relation to the first said member, and a fourth member adapted to overlie both the second and the third said members, said fourth member being movable in relation to said second and third members and having inscribed thereon segregate markings adapted for cooperation respectively with one each of said face markings whereby when al1 of the aforesaid members occupy a particular position the markings thereon indicate the relationship between several factors of a given problem.

10. Ina calculator, a first member, a second member pivoted to said first member, said second member having inscribed thereon markings adapted for cooperation with markingson said first member, a third member pivoted to said rst member, said third member having inscribed thereon markings adapted for cooperation with other and difiere t markings inscribed on said first member an having its pivot axis spaced from the pivot axis of said second member, and a fourth member pivoted to the first said member, said fourth member having inscribe d thereon markings adapted for cooperation respectively with other and further markings inscribed on the second' and third members respectively, and having its pivot axis in coincidence with one of the two pivot axes aforesaid whereby-when all of the aforesaid members occupy a particular position the markings thereon indicate the relationship between several factors of a given problem.

11. In a calculator, a first member having inscribed thereon twofamilies of curves, a second member movable in relation to said first member and having inscribed thereon markings adapted for cooperation with one of said families, of curves, a third member movable in relation to said first member and having inscribed thereon of said families of curves, said second and third members each having inscribed thereon one or more curves, and a fourth member movable in relation to the other three members, said fourth member having inscribed thereon markings or more curves inscribed on the second and third members whereby when all of the aforesaid members occupy a particular position the markings thereon indicate the'relationship between several factors of a given problem.

l2. In a calculator, a first member having inscribed thereon a curve, a second member movable relatively to` said first member, said second member having 'cupy a particular position the markings thereon indicate the relationship between several factors of a given problem.

13. In a calculator, a first member provided with two groups of markings, a second member rotatable in relation to said first member, said second member having inscribed thereon a family of curves and also a marking adapted for cooperation with one of said groups of markings, a third member rotatable in relation to said first member, said third member having a marking adapted to cooperate with the other of said groups of markings said second and third members having a common axis of rotation and means rotatable with andadjustable in its relation to said third member, said means having inscribed thereon markings adapted for cooperation with said family of curves whereby when all of the aforesaid` members occupy a particular position the markings thereon indicate the relationship between several factors of a given problem.

14. In a calculator, a first member, a second member pivoted to said first member, said second member having inscribed thereon a family of curves, a third member pivoted to said first member, said third member having inscribed thereon a curve, said second and third members having their pivot axes disposed in spaced relation, and a fourth `member mounted on said first member and rotatable in relation to the second and third members, said fourth member having scales inscribed thereon adapted for cooperation respectively with the curves inscribed on the second and third members, the pivot axis of said fourth member being in coincidence with one of the pivoted axes aforesaid whereby when all of the aforesaid members occupy. a particular position the markings thereon indicate the relationinscribed thereon markings,

adapted for cooperation with said curve and alslzi'65 having inscribed thereon a curve, a third mermber movable relatively to said first and second members, said third member having inscribed thereon a curve, and a fourth member movable 70 in relation to the other said members and having inscribed thereon segregate markings adapt``\`` ed for cooperation respectively `with the curves inscribed on the second and third members first membe scribed thereon segre whereby vwhen all of the aforesaid members ocship between several factors of a given problem. i l5. In a calculator, a first member having inscribed thereon a family of curves, a second member pivoted to said first member, said second member being provided with edge markings adapted for cooperation with said family of curves and having inscribed on its face a curve,

and a third mlember'pivoted to said first member, said third' member having its pivot axis off- ,set in relation to the pivot axis of said second l' lmember and havinginscribed thereon edge mark- ,ings adapted for cooperation with the curve inscribed on said second member whereby when all of the aforesaid members occupy a particular position the markings thereon indicate the relationship between several factors of a given problem.

16. Ina calculator; a first member having inscribed` thereon segregate markings representing two different factors; a second member fastened to and movable relatively to said first member, said secondfmember having inscribed thereon segregate markings representing two different factors, one of which said markings is adapted to cooperate with one of the markings on said first lmember; a third member fastened to and movable relatively to said first member, said third member having inscribed thereon segregate markings representing two different factors, one

of which is adapted to cooperate with the` other of the markings on said first member; and a fourth member movable relatively to said second and third members as well as relatively tosaid gate markings representing two different factors adapted 'to cooperate respectively with the markings on said second and r, said fourth member having inthird members whereby when all of the aforesaid members occupy a particular position the markings thereon indicate the relationship between several factors of a given problem.

17. In a calculator; a rst member having inscribed thereon segregate markings representing three different factors; a second member fastened to and movable relatively to said first member, said second member having inscribed thereon segregate markings representing two different factors, one of which said markings is adapted to cooperate with one of the markings on said first member; a third member fastened to and movable relatively to said first member, said third member having inscribed thereon segregate markings representing two different factors, one of which is adapted to cooperate with one of the other markings on said first member; and a fourth member fastened to said first member and movable relatively to said second and third members as well as relatively to said first member, said fourth member having inscribed thereon segregatemarkings representing three different factors, one of which is adapted to cooperate with the third of the markings on said first member and the remaining two respective-ly with the other of the markings on said second member and on said third member whereby when all of the aforesaid members occupy a particular position the markings thereon indicate the relationship between several factors of a given problem, l

18. In a calculator; a first member having inscribed on its face a family of curves representing one factor, a second member pivoted to said first member and provided with edge markings adapted for cooperation with said family of curves and having inscribed on its face a family of curves representing a different factor; and a third member pivoted to said first member, said third member and said-,second member having a common pivot axis and said third member being provided with an edge marking adapted for cooperation with the family of curves of said second member whereby when all of the aforesaid members occupy a particular position the markings thereon indicate the relationship between several factors of a given problem.

19. In a calculator; a first member having inscribed thereon a family of curves representing one factor and also markings representing a different factor; a second member pivotedto said first member, said second member having inscribed thereon segregate markings one of which is adapted for cooperation with said family of curves; and a third member pivoted to said first member, said third member having inscribed thereon segregate markings adapted to cooperate respectively with the other of the markings on said first member and on said second member whereby when all of the aforesaid members occupy a particular position the markings thereon indicate the relationship bet'ween several factors of a given problem.

20. In a calculator; a first member having inscribed thereon'two families of curves; a second member mounted on and movable in relation to said first member, said second member having inscribed thereon segregate markings one of which is adapted to 4cooperate with one said family of curves; and a third member movable in relation to said first and said second members, said third member having inscribed thereon segregate markings adapted to cooperate respectively with the other said family of curves and with the other of the markings on said second member whereby when all of the aforesaid members occupy a particular position the markings thereon indicate the relationship between several factors of a given problem.

21. In a calculator; a first member; a second member rotatable in relation to said first member, said second member having inscribed thereon a face marking; a third member rotatable in relation to said first member, said third member having inscribed thereon a face marking; and a fourth member adapted to overlie said second and third members and rotatable in relation thereto, said fourth member having inscribed thereon segregate markings adapted to cooperate respectively with the face markings on said second and third members, the axis of rotation of said fourth member being in coincidence with the axis of rotation of one of the other of said rotatable members whereby when all of the aforesaid members occupy a particular position the markings thereon indicate the relationship between several factors of a given problem.

22. In a calculator; a first member having inscribed thereon segregate markings, one of which saidmarkings comprises a family of curves; a

`second member mounted on and movable in relation to said first member, said second member having inscribed thereon segregate markings, one of which said markings is adapted to cooperate with one of the segregate markings on said first member; and a third member movable in relation to said first and said second members, said third member having inscribed thereon segregate markings adapted to cooperate respectively with the other of the markings on said first member and with the other of the markings onsaid second member whereby when all of the aforesaid members occupy a particular position the markings thereon indicate the relationship between several factors of a given problem.

23. In a calculator; a first member having inscribed thereon segregate markings; a second member mounted on and movable in relation to said first member, said second member having inscribed thereon a family of curves; and a third member movable in relation to said first and said second members, said third member having inscribed thereon segregate markings adapted to cooperate respectively with the segregate markings on said first member and with the family of curves on said second member whereby when all of the aforesaid members occupy a particular position the markings thereon indicate the relationship between several factors of a given problem.

ARTHUR L.r THURSTON. BEAUREGARD SWEENEY. 

